A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

Wagner, Gregory John (Sandia National Laboratories, Livermore, CA) ; Collis, Samuel Scott ; Templeton, Jeremy Alan (Sandia National Laboratories, Livermore, CA) ; Lehoucq, Richard B. ; Parks, Michael L. ; Jones, Reese E. (Sandia National Laboratories, Livermore, CA) ; Silling, Stewart Andrew ; Scovazzi, Guglielmo ; Bochev, Pavel B.

Sandia National Laboratories

关键词: Molecules Mathematical Models.;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Computerized Simulation;    Atoms;    Scaling Laws;   

DOI  :  10.2172/922756
RP-ID  :  SAND2007-6179
RP-ID  :  AC04-94AL85000
RP-ID  :  922756

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来源: UNT Digital Library

【 摘 要 】

This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.